Abstract
We consider two notions of purity in categories of sheaves: the categorical and the geometrical. In case the scheme X is quasi-separated we construct a model category structure in \(\mathbf {C}(\mathfrak {Qcoh}(X))\), the category of chain complexes of quasi-coherent \(\mathcal {O}_X\)-modules, that yields the geometrical pure derived category of \(\mathfrak {Qcoh}(X)\).
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E. Enochs, S. Estrada, S. Odabaşı, Pure injective and absolutely pure sheaves. Proc. Edinb. Math. Soc. 1–18 (2013)
S. Estrada, J. Gillespie, S. Odabaşı, Pure exact structures and the pure derived category of a scheme. Preprint available at arXiv:1408.2846
S. Estrada, M. Saorín, Locally finitely presented categories with no flat objects. Forum Math. 27(1), 269–301 (2015)
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Estrada, S. (2016). Purity in Categories of Sheaves. In: Herbera, D., Pitsch, W., Zarzuela, S. (eds) Extended Abstracts Spring 2015. Trends in Mathematics(), vol 5. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-45441-2_10
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DOI: https://doi.org/10.1007/978-3-319-45441-2_10
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-45440-5
Online ISBN: 978-3-319-45441-2
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